Thread: "IRP {4,6} VT solved"

Hi all,
today I tried to solve {4,6} (12 colors, vertex-turning) in IRP mode. It =
was hard enough. One twist touches about 1/3 of puzzle pieces (almost as in=
3^3), and at the first glance, two intersecting circles have two areas of =
intersection. But some investigation revealed that actually number of eleme=
nts in this puzzle is not 92 (as expected), but only 50: all non-vertex pie=
ces are grouped in rigid pairs of elements symmetric with respect to any ve=
rtex (in surface geometry). For example, what we see as central grey centra=
l element is actually a half of grey-light_blue 2C piece. Edge elements are=
actually 4C, and petal elements are also grouped in pairs - but again, gre=
y color is grouped only with light blue. So we can swap these elements... b=
ut not every pair of them - there are two orbits of petal stickers. I notic=
ed it too late and spent some time trying to find setup moves that are actu=
ally impossible.
Result is 517 twists. It was only 25-twist scramble, but I didn't see any=
shortcuts, so it was like full-scrambled for me.

Andrey

{6,6}, 4 colors was easy - I think that it is some equivalent to pyraminx. =
But now I'm looking at {6,4} FT - and it is a monster!



--- In 4D_Cubing@yahoogroups.com, "Andrey" wrote:
>
> Hi all,
> today I tried to solve {4,6} (12 colors, vertex-turning) in IRP mode. I=
t was hard enough. One twist touches about 1/3 of puzzle pieces (almost as =
in 3^3), and at the first glance, two intersecting circles have two areas o=
f intersection. But some investigation revealed that actually number of ele=
ments in this puzzle is not 92 (as expected), but only 50: all non-vertex p=
ieces are grouped in rigid pairs of elements symmetric with respect to any =
vertex (in surface geometry). For example, what we see as central grey cent=
ral element is actually a half of grey-light_blue 2C piece. Edge elements a=
re actually 4C, and petal elements are also grouped in pairs - but again, g=
rey color is grouped only with light blue. So we can swap these elements...=
but not every pair of them - there are two orbits of petal stickers. I not=
iced it too late and spent some time trying to find setup moves that are ac=
tually impossible.
> Result is 517 twists. It was only 25-twist scramble, but I didn't see a=
ny shortcuts, so it was like full-scrambled for me.
>=20
> Andrey
>

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Thank you for this analysis Andrey! It was delightful to read, and to
follow along with the puzzle open, reproducing the behaviors. I think my
colors might be mapped differently (gray is not opposite light blue for
me), but I could see everything you describe :)

Roice


On Tue, Dec 13, 2011 at 6:34 AM, Andrey wrote:

> Hi all,
> today I tried to solve {4,6} (12 colors, vertex-turning) in IRP mode. It
> was hard enough. One twist touches about 1/3 of puzzle pieces (almost as in
> 3^3), and at the first glance, two intersecting circles have two areas of
> intersection. But some investigation revealed that actually number of
> elements in this puzzle is not 92 (as expected), but only 50: all
> non-vertex pieces are grouped in rigid pairs of elements symmetric with
> respect to any vertex (in surface geometry). For example, what we see as
> central grey central element is actually a half of grey-light_blue 2C
> piece. Edge elements are actually 4C, and petal elements are also grouped
> in pairs - but again, grey color is grouped only with light blue. So we can
> swap these elements... but not every pair of them - there are two orbits of
> petal stickers. I noticed it too late and spent some time trying to find
> setup moves that are actually impossible.
> Result is 517 twists. It was only 25-twist scramble, but I didn't see any
> shortcuts, so it was like full-scrambled for me.
>
> Andrey

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